help-36

[vital crag]

My statement was a general statement and not the same x as the video's

This is different and a general statement

[granite grove]

ohhh later he says we just want top half of the circle thats why?

so its positive value not negative

[vital crag]

sqrt(1-x^2) is the top half of the unit circle yes

,w plot sqrt(1-x^2)

[soft zealot]

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[vital crag]

Ugly scale, but you should get the idea

[granite grove]

okay thats why he cancels sqrt with squared right?

if it was bottom half then he wouldnt have done that

[vital crag]

The bottom half of the circle has a different equation

Guess what it is

[granite grove]

with the - sign?

it will be x^2+y^2=-1

[vital crag]

No

,w plot - sqrt(1-x^2)

[soft zealot]

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[vital crag]

This equation has no solutions in the reals

[granite grove]

,w plot x^2+y^2=-1

[soft zealot]

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[granite grove]

oh

LOL

[granite grove]

oh okay

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[dusk atlas]

ive been working on this problem for a bit and im really confused how to set up the integral. im not sure if it should be a triple integral or double. i feel like i may need to split the problem into two seperate integrals but im really not sure

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[runic tulip]

8*6 isn't 56

[vernal bloom]

oh

right

my bad

[runic tulip]

Sorry just woke up

[vernal bloom]

all good

[runic tulip]

Np

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[chrome hemlock]

how do i do part B

[chrome hemlock]

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[final saddle]

Please don't occupy multiple help channels.

[chrome hemlock]

Can someone pls help me I suck at these questions

[cyan kayak]

@chrome hemlock Multiply out the left first

[mental roost]

1 - cos + 1/cos - 1 = sin tan
1/cos - cos = sin tan
1 - cos^2 = sin^2
1 = sin^2 + cos^2

[chrome hemlock]

how do i get better at them

[chrome hemlock]

oh

how did u know to do that one

instead of rhs

[mental roost]

Left side was more complicated

[fringe sigil]

lhs will be easier

[cyan kayak]

You could to either

But lhs is more complicated, so it's more likely to simplify

And simplifying tends to be easier

[chrome hemlock]

oh

[cyan kayak]

Than complexifying in exactly the correct way

[chrome hemlock]

so i pick the one that looks harder

[mental roost]

Yes, but just try everything honestly

[limpid egret]

More like - prove that the complicated one is equal to the simplified one

[fringe sigil]

well.. u cant really decide like this, but when u sometimes do these, u find that many terms cancel each other and u get a simpler version

[chrome hemlock]

wow that was easier

thx guys

uh.. how do I find inverse tan of root 3 again

[cyan kayak]

@chrome hemlock tan(x) = opposite/adjacent

What is the angle of a right triangle where the opposite side is √3 and the adjacent side is 1?

[chrome hemlock]

how are u supposed to know

[cyan kayak]

That's a special type of triangle

Normally you don't know

[chrome hemlock]

oh I can do this

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[robust girder]

hi

[robust girder]

how do i do 4b?

[cyan kayak]

How did you do 4a, out of curiosity.

[robust girder]

i did 5 over 0.2

[cyan kayak]

Maybe I'm misinterpreting "frequency density"

Anyway, you need to be able to sum up all of the data on the graph, but the values are not provided.

[robust girder]

So is it not possible?

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[thin shard]

how do you prove that M E and F are on the same line

E and F are in the middle of their lines if that wasnt clear

[cobalt kettle]

maybe ME and EF shud have the same gradient?

[thin shard]

ok one min

does that prove it?

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[thin shard]

i still need help

i dont know how its proved

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[thin shard]

<@&286206848099549185>

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@thin shard Has your question been resolved?

[thin shard]

:(

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[zealous yoke]

can someone help me w this

do i sub pi/3 straightaway when i do the first derivative ?

im not rlly good w trig

[mossy cobalt]

derive two times n plug in pi/3

[zealous yoke]

is this right ?

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[limpid breach]

I need help calculating average acceleration and average force for my vertical jump. The measurements I have to work with are:

Mass= 7.3kg
Height with arm raised= 1.93 m
Height squatted with arm raised= 1.8m
Jump height= 2.24 m
Launch Velocity= 0.64 m/s

I don't think we're allowed to use time so I'm not quite sure how to get acceleration and force. Is it even possible to?

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@limpid breach Has your question been resolved?

[limpid breach]

<@&286206848099549185>

[limpid breach]

I mean you can find average acceleration with initial velocity, final velocity, and displacement but isn't my initial velocity 0.64 and my final velocity -0.64.

<@&286206848099549185>

[glacial wharf]

the average velocity is the( inital velocity + the final velocity)/2

[glacial wharf]

so just plug that in

[limpid breach]

But don't I need time as well if I do that?

[limpid breach]

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[tranquil pine]

I'm confused on this question on my practice exam and I think that this problem doesn't have enough information to be solved

[shut gazelle]

It has enough

Hint: complementary angles

You're given the right angle symbol

[tranquil pine]

I don't have that notepacket with me

[shut gazelle]

Google it

[tranquil pine]

Ok

90 degree angle

[shut gazelle]

What about 90 degrees?

[tranquil pine]

So 90-41

[shut gazelle]

Yes

[tranquil pine]

= the answer

So the answer is 49

Right?

[shut gazelle]

Yep

[tranquil pine]

Thank you

😁

Close

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[ancient basalt]

No clue how to start

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[kind crane]

i understand how to do the problem here, but im not sure why x is squared at the end

could anybody please explain why?

[fallow yacht]

The question asks for the square of the distance

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[sour kindle]

I’m stuck at this point, can someone guide me the right answer. It’s been a while since i did limits all i could figure out is that congruent would help.

[stone wagon]

make a substitution

let u=e^x

as $x\to\infty$, $u\to\infty$

[soft zealot]

artemetra

[stone wagon]

so you just get $\lim_{u\to\infty}(\sqrt{u^2 - u} - u)$

[soft zealot]

artemetra

[stone wagon]

can you take it from here?

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[spring thunder]

Good afternoon I have this incredible exercise that I need help with

[spring thunder]

Exercise 5 it is

I don't have any idea where to even start

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[spring thunder]

<@&286206848099549185>

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[stone wagon]

let B be an upper bound of the sequence, since you know it's bounded

can you use that formula with B somehow?

[spring thunder]

Well I managed to solve it one way or another. I think, I took another seq bn=ln(an)

Then I bounded bn with cn that's the max of bn and bn-1

Substituted bn and bn-1 with cn

And bn+1 with cn+1

We got that cn is bounded and non increasing

Which means it is convergent

And bn is included into cn then it is convergent to the same limit

And the inf of bn is ln(inf{an}

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[radiant vale]

Jake borrowed PHP 25,000 from M.O.N.E.Y. Lending corporation. He agreed with the corporation's policy of 3.50% simple interest rate. If he needs to pay his debt in 1 year and 6 months, how much is the simple interest accumulated?

[white sphinx]

do you know the formula for simple interest?

[radiant vale]

is it I = p x r x t

[white sphinx]

yes

[inland kettle]

yes

[radiant vale]

so 25000 x 0.035 x 1.5

[white sphinx]

yes

[inland kettle]

mhm

might be helpful to write that as 35/1000

[radiant vale]

I got 1312.5

[white sphinx]

correct

[radiant vale]

what is the hundreths

[white sphinx]

wut

[radiant vale]

for the decimal position

[inland kettle]

,calc 250000.0351.5

[soft zealot]

Result:

1312.5

[inland kettle]

correct, yay

no hundredths

[radiant vale]

oh okei

[white sphinx]

well

[radiant vale]

is this correct

[white sphinx]

its just 0

yes

[radiant vale]

so the answer is c?

[inland kettle]

you've marked b

;-;

[radiant vale]

yeah but is c the correct answer?

or my answer (b) is correct?

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[agile flume]

I forgot how to do right triangles can someone help

[agile flume]

If I don’t respond please leave the answer and show me how you got it

[drowsy epoch]

1 Method is pythagoras

It is applicable for right triangles

Now since you are given angles, you can also make use of trignometry, if that says something to you

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[unique moss]

1. pythagoras, 2) sin/cos theorem, 3)known 30 60 90 triangle

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[radiant vale]

how to do this

[ancient basalt]

Basically the sum of squares from 1 to 18

[radiant vale]

then

[ancient basalt]

We can take 17 common

[ancient basalt]

Just use the formula

For sqaures of n natural numbers

[runic tulip]

do you know sum of squares of first n natural nums?

[radiant vale]

unfortunately nope

😭

[ancient basalt]

Well that's the simplest way to do this

[runic tulip]

use the second equal to

n(n+1)(2n+1)/6 one

[scarlet sequoia]

top 10 screenshots cut short

[runic tulip]

this is better

[radiant vale]

wait let me try

[runic tulip]

i just right clicked and copied 💀

[scarlet sequoia]

welp bad

[runic tulip]

follow this onee

[radiant vale]

18
∑ n^2 = 18(19)(37)/6 = 12654/6 = 2109
n=1

17 * 2109 = 35853

[ancient basalt]

Seems correct

[radiant vale]

thank uu

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[delicate rapids]

hi

[delicate rapids]

hi evone

does anyone have solution for this?

[pliant shore]

okay, this is an example of the Chinese remainder theorem

so you have that N = 9k + 6 for some integer k

oh wait, do you know modular arithmetic?

[delicate rapids]

oh not really

wait

i think i do

(a)= a=-1 or 1

sorta thing

[pliant shore]

okay then $9k + 6 \equiv 10 \pmod {11}$

[delicate rapids]

right the mod can have two thing

[pliant shore]

yeah working with congruences

[soft zealot]

south's secret twin brother

[pliant shore]

there aren't exact steps to realise this but then $-2k \equiv 4 \pmod 11$

[delicate rapids]

i m sorry but

[soft zealot]

south's secret twin brother

[delicate rapids]

what is the three lines

and mod

has do

do here

[pliant shore]

equivalent to

9k + 6 has the same remainder as 10 when divided by 11

[delicate rapids]

oh so things that divisible 11

ohhhh

ic

[pliant shore]

yeah, remainders when dividing by 11

so the key thing is that 9 leaves the same remainder as -2

cause 9 - 11 = -2

[delicate rapids]

how did we get to this?

from the mod thing to here?

[pliant shore]

this

and then we can subtract 6 on both sides

[delicate rapids]

oh

i m sorry

but

how did we go from 9k+6=10 mod 11 to

[pliant shore]

okay maybe try a different approach then

[delicate rapids]

-2k

thing

[delicate rapids]

nono it's okay

[pliant shore]

you can replace 9 by -2 since they leave the same remainder mod 11

[delicate rapids]

i m okay with this approach

[pliant shore]

you sure?
I was going to suggest that you consider the numbers 10, 21, 32...
the numbers that leave remainder 10 when divided by 11

[delicate rapids]

oh why do they leave the same remainder

[delicate rapids]

sure

sure

i like that way

[pliant shore]

so considering the remainders modulo (when divided by) 9

we get 1, 3, 5......

each time we are adding 2

(it's cause when we add 11, it leaves the same remainder as 2)

[delicate rapids]

ahhhhhh

that;s why we can

replace 9 by

[pliant shore]

so if you continue you get 1, 3, 5, 7, 0, 2, 4, 6

when we add 7 + 2 = 9 then divide by 9

[delicate rapids]

-2?

[pliant shore]

we get a remainder of 0

[pliant shore]

right, cause it's no different when we count backwards

when we subtract 11, we are subtracting 2

[delicate rapids]

i see

so we can basically replace

9 with -2

[pliant shore]

yep

[delicate rapids]

bc it's the difference between

11 and 9

[pliant shore]

yeah

9 is 2 less than 11

so -2

[delicate rapids]

so??

what happen next?

[pliant shore]

so 6 is the 8th number
ah wait, but in the 1st number we have added zero 11s
in the 2nd number we have added one 11

you should be able to figure out N from this

by completing the pattern

[delicate rapids]

so basically

1 3 5 7 0 2 4 6 8 10

[pliant shore]

yeah that's the whole cycle

we stop when we get 6

[delicate rapids]

why tho?

thx for the explanation

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[pliant shore]

cause of the question, we want the remainder to be 6 when divided by 9

all these numbers have remainder 10 when divided by 11 already

[delicate rapids]

thx

for ur help

.close

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✅

[delicate rapids]

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[turbid lake]

I know how to do slope and intercept ( I think ) but uh what's it mean form

[marble quest]

you have different forms of the equation of a slope

you have normal

you have intercept

[turbid lake]

There's like special purpose, y=mx+b and normal

There's 3 I gotta choose between

[marble quest]

yea

then theres also

x/a+y/b=1

[turbid lake]

Uh yeah we ain't learn that yet 😭

[marble quest]

yes i suppose

[turbid lake]

But how do I determine which one

[marble quest]

oh then whatever you've learned

[turbid lake]

Because I'm lowk cooked

Well I know y=mx+B

[marble quest]

if you plot the line

i suppose with that you can derive the formula of the slope

therse also one point and two point formulas for the slope

do you know?

[turbid lake]

Not really

[marble quest]

ok well solve the function

[turbid lake]

I know that you can find slope with the intercepts

[marble quest]

yea

[turbid lake]

Which is number 14 and 17 right

[marble quest]

where?

[turbid lake]

This

[marble quest]

sure

[turbid lake]

So what would I call the form on finding the intercepts

[marble quest]

oh the question says state the form of the function

ok that makes it easier

[turbid lake]

Special purpose or normal

[marble quest]

ok so for question 12

you have

(y-y1)=m(x-x1) i suppose

thats your form

[marble quest]

wait tell me what forms you've learned

[turbid lake]

Special purpose, y=mx+b and like slope intercept form

[marble quest]

also if you haven't learned x/a+y/b=1 then

im pretty sure you haven't learned normal form either

cus normal form is xcosalpha+ysinalpha=p

[marble quest]

gimme special purpose rq

[turbid lake]

Well for 12 we had to switch the -1 in the () to a 1 so then we got 1, -4 for starting point

[marble quest]

yea makes sense

[turbid lake]

So that would be like the form we used

[marble quest]

y=mx+B

open the brackets you basically get that formula

r u good with functions?

[turbid lake]

Maybe idk 😭

[marble quest]

ok wait give me the inverse of this

f(x)=4x-3

[turbid lake]

Don't know what inverse is

[marble quest]

f-1(x)

or nvm thats alright too

ok so move onto question 13

how would you go about that one

[turbid lake]

For slope it's -2 and starting point is -5

So then I can go up 2, left 1 and over and over

Then I find the intercepts

[marble quest]

ok so you get it?

[turbid lake]

Yes

[marble quest]

lmfao ok

btw i learned this topic this morning

[turbid lake]

Only thing I don't know is the silly form things 😔

[marble quest]

did u miss school

or did they only teach you three forms

[turbid lake]

No

We have substitute for 6 weeks

[marble quest]

oh makes sense

6 weeks is long man thats gonna be tuff

[turbid lake]

I'll lock in

[marble quest]

good luck

[turbid lake]

Alright well I think I'ma just ask the teacher but thank you for helping

[marble quest]

sure

[turbid lake]

Have a good day

.close

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[marble quest]

you too

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[plush prairie]

hello! when i try to factor using my fx991 calculator i get a different answer from what i factored as an example this equation 2x^2-7x+3 now when i do it i get 2x-1 and x-3 but when i do it on the calc i get x=3 and x=0.5 can someone help?
ax^2+bx+c

[warm wraith]

The calculator gives you the roots, not the factors themselves

[plush prairie]

wym

[warm wraith]

Like, your calculator gives you the values of x for which the polynomial = 0

[plush prairie]

but i wanna make sure that the factorization i did is correct right?

no

i use mode 5,3

[rustic light]

how did you get 2x-1 and x-3?

[plush prairie]

which is EQN then i choose the ax^2+bx+c=0

[plush prairie]

i factorized

[rustic light]

it's correct

but the calculator gave you the roots

[plush prairie]

yeah i know but i wanna use the calc

[rustic light]

not the factorization like he said

you could do it backwards with the calculator

[plush prairie]

so like i get a positive 3 i turn it to negative 3

[rustic light]

yea, so you'd have (x-3)(x-1/2), but since the coefficient a is 2 then it's (x-3)(2x-1)

[scarlet sequoia]

!occupied

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[dense garnet]

Does anyone know why Rudin put x>0 rather than x>=0?

I'm interested in knowing if the theorem applies to x=0.

[tranquil pine]

think about what happens when x = 0

[supple jacinth]

.help

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[cloud grail]

i think its because 0 is rather unique due it being the multiplicative identity in the feild R

[dense garnet]

I think I understand, there can't probably be a positive y then, but why can't there be?

[tranquil pine]

the statement is not applicable not because of the nature of the field R, but rather because, although there is a solution y = 0, it does not meet the requirement of being positive, hence rendering the statement inapplicable to this case

[dense garnet]

ok

[tranquil pine]

have you heard of a positive real number which, raised to an integer power gives 0?

(I haven't)

[dense garnet]

I see 🙂

[cloud grail]

ah i see that makes sense thanks 😄

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[light flicker]

H

[light flicker]

Pls help

[plain star]

hell no 💀

math on tik tok

[light flicker]

😭😭😭

[vital crag]

Why is there so much in this image

[fathom walrus]

||(Whenever you see ‘A level maths’ just ignore)||

[cloud grail]

accurate

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@light flicker Has your question been resolved?

[light flicker]

How come

[light flicker]

Idk

I got x=-0.5

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[tranquil pine]

I got that Dg(f(x)) = (-inf,0) U (1,4/3) U (4/3,+inf)

I need someone smarter to confirm please :)

If you need the formula for the domain of a composite function for easier solving:

Dg(f(x) = {x ∈ Df | f(x) ∈ Dg}

Or, in words: The domain of the composition g(f(x) equals the intersection of x in the domain of f and f(x) in the domain of g

<@&286206848099549185>

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[tranquil pine]

@everyone

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[worthy cloud]

Hello

[worthy cloud]

I'm working on a project where I need to filter out which is the actual product based on the prices

For example

The iPhone cover cost 25€ but the actual I phone costs 100€

How do I tell that the I phone cover isn't a good product because it's way too cheap to be true

Mathematically

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[wicked kernel]

how do i start this?

[wicked robin]

Well do you have a candidate for the limit?

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[wicked robin]

?

[final saddle]

@wicked kernel Has your question been resolved?

[wicked kernel]

i don’t get a candidate

[wicked robin]

I’m asking for you to decide on one

That’s how you start

[wicked kernel]

what’s candidate

[wicked robin]

An educated guess

Like what is the limit intuitively?

[wicked kernel]

why can’t i use squeeze theorem here

[wicked robin]

You do that when you have a candidate for the limit

You can’t otherwise start, or else you’re just shooting blank

[wicked kernel]

the candidate is x?

[wicked robin]

Is that what you think the limit is? The letter x?

Have you computed limits before?

[wicked kernel]

the candidate is (1,2,3)

[wicked robin]

I’m basically asking you to compute the limit as you would normally do

That will be our candidate for the limit, i.e what we believe is the limit

[wicked kernel]

ah

i see

the candidate is -4

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[subtle urchin]

Find the roots of the polynomial given that they are reciprocal

[subtle urchin]

!status

[final saddle]

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1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[subtle urchin]

2

i know:

a: 2k + 2

b: 4-4k

c: k-2

and X1*X2 (the roots) = 1

also i think i found the value of K to be 1 but idk

<@&286206848099549185> pls help

[drowsy tulip]

Yes

[subtle urchin]

what is yes

😭

[drowsy tulip]

You tagged

I said yes

What do you want help for

[subtle urchin]

like yes as a question

yes?

Find the roots of the polynomial given that the roots are reciprocal

[drowsy tulip]

I’ll see

To find the roots of the polynomial ( (2k + 2)x^2 + (4 - 4k)x + k - 2 = 0 ) with the condition that the roots are reciprocal, we can use the fact that if the roots are reciprocal, then their product is 1.

Let the roots of the polynomial be ( p ) and ( \frac{1}{p} ). From Vieta's formulas, the product of the roots is the constant term divided by the leading coefficient, which in this case is ( \frac{k - 2}{2k + 2} ).

Since the roots are reciprocal, we have ( p \times \frac{1}{p} = 1 ), which implies ( p^2 = 1 ), leading to ( p = \pm 1 ).

Therefore, the roots of the polynomial are ( x = 1 ) and ( x = -1 ).

[soft zealot]

rich life

[subtle urchin]

that is wrong though

[drowsy tulip]

How?

I’m sorry

[subtle urchin]

1 and -1 arent roots of the polynomial

[drowsy tulip]

I’m still in grade 12

[subtle urchin]

[drowsy tulip]

Real

Wait

Why don’t you use Ai

[subtle urchin]

ive tried

cant seem to be able to solve this one

also ai is bad at math

i only use it last resort and im always left disappointed

[gentle barn]

Is this given, or did you find out on your own?

[subtle urchin]

given

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[dusk laurel]

how would you differentiate this

[dusk laurel]

nvm no x on top

[distant sleet]

chain rule

[dusk laurel]

i completely forgot abt that tysm

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[radiant vale]

2500 was deposited in a bank account, 10 years ago. Today it is worth 5,000 pesos . Interest is paid semi annually. Determine the interest rate paid on this account

[cyan kayak]

@radiant vale are you aware of the F/P formula?

Alternatively, if that is not something you've studied, then are you aware of how interest works more generally?

[radiant vale]

I only know this formula A = P * (1+R/N)^N *T

i dont know how to solve

[cyan kayak]

@radiant vale so you know T, N, P, and A

And you want to solve for R

Do you understand why?

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[worn sluice]

when a problem says "|f'(x)| >= |g'(x)| for any x", does this mean the x you input into both f and g are the same or is it saying |f'(x)| is always greater or equal to |g'(x)|

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[gusty geode]

Help

[gusty geode]

18

<@&286206848099549185>

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[gusty geode]

I think I got it

Gimme a sec

[limpid egret]

You should

It's a matter of 4 lines max

[gusty geode]

Got it

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[tropic nymph]

Hey can someone help me solve this

[tropic nymph]

I know that the formula of logarithmic differentiation is f(x) * d/dx ln(fx)

but after this I am stuck on how to solve this

[terse crypt]

?

u take ln both sides

let me show u first step

[tropic nymph]

that is the formula of logarithmic differentation right

[terse crypt]

Ye

[terse crypt]

U can take partial differential for y next

[tropic nymph]

I understand this step and then I don't understand what is happening after

[terse crypt]

i take partial dif with respect to x on both sides

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[regal hamlet]

$A$ is a set. Show that $\partial A = \bar A \setminus \text{int}(A)$

[soft zealot]

Halex

[regal hamlet]

The definition of the Boundary $\partial A$ I have is that $\partial A = \bar A \cap \bar A^c$

[soft zealot]

Halex

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[scarlet sequoia]

you mean $\bar A \cap \overline{A^c}$?

[soft zealot]

rafilou is not not born in 2003

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[indigo plover]

numbeers and exponents are involved plz

[indigo plover]

how come

the 3d^7 go to 3d^6 😦

i understand the 4s^2 to 4s^0 becuz it has larger n value

[boreal locust]

its 3+

so like

3 electrons are out

first it went out from s

the 2 electrons

[indigo plover]

Oh

[boreal locust]

then 1 electron went out from d

[indigo plover]

Makes sense

Perfect thnxs

[mystic tapir]

should have been 4s1 3d5 i think

[indigo plover]

wot

[boreal locust]

no

[mystic tapir]

stability?

[boreal locust]

what stability

[indigo plover]

d can have 5-10 e- to be stable right?

[boreal locust]

its in excited state

the cromium config doesnt apply to here

[mystic tapir]

ohk

[indigo plover]

Well thnxs that cleared it up

.close

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[zealous storm]

I don't have answers to this but is my argument correct

draw an altitude from A and call it D

by pythag, AB > AD > BC

and to show AB > AC:

1. AD^2 + DC^2 = AC^2

2. AD^2 + DB^2 = AB^2

DB^2 - DC^2 = AB^2 - AC^2 > 0 because DB = DC + CB and both DC, CB > 0

so AB > AC

[dense coral]

did you mean to say AB > BD > BC?

[zealous storm]

yes

i think it's right,no?

[dense coral]

looks good to me!

[zealous storm]

thanks

can i get verification on this too

this one though i got an opposite result

lol

<ADC = <C < 90 cuz acute triangle

and so <ADB is the supplementary angle of <ADC and should be > 90

since <B < 90 then <ADB > <B

[dense coral]

yeah I can't be asked to check geometry rn, sorry >.<

[zealous storm]

😭 oh

okay no problem

i hate geometry too

i'm so close to being done

[dense coral]

you'll have to wait for someone else

[zealous storm]

after that i'll never touch geometry either

[dense coral]

this kind of geometry makes me sad

[zealous storm]

😭 i just care about the result

not really about proving it

for this case at least

seems boring

[dense coral]

these proofs kinda suck ngl

[zealous storm]

fr 😭

[hollow sorrel]

proof: draw a diagram and it's obvious

[zealous storm]

BUT HOW?

sorry caps lol

😭

my diagram works

but

[hollow sorrel]

no i mean proving ur result lol

[zealous storm]

how about this

[hollow sorrel]

as in this is one of the weird geo proofs cus the result is just kinda obvious

[zealous storm]

<ADC = <C < 90 cuz acute triangle

and so <ADB is the supplementary angle of <ADC and should be > 90

since <B < 90 then <ADB > <B

[zealous storm]

oh

Lol speaking about obvious proofs

This is so stupid

but can you help me check my "glitch"

with this diagram it's obvious:

<D < <B and so <DAX > < BAX

https://cdn.discordapp.com/attachments/908076393198419988/1298695930551341086/image.png?ex=671a8056&is=67192ed6&hm=aafc47338bc9e0c679a208ffffc8f52ea6fff4076b82515fdb8a074de0c0aae1&

but with this diagram you get a different result,namely (<DAX) < (<BAX)

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[restive beacon]

I need to solve this Matrix !

How do i start

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[vital crag]

!original

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

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[nimble trench]

Sorry to repeat the question but the channel was automatically closed.

in the context of matrix transformations with the Gaussian elimination method this (2,1;-1) corresponds to: row 2 = -1 * row 1 + row 2?

[nimble trench]

if the question is not clear I try to elaborate again

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[nimble trench]

<@&286206848099549185>

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.close

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[runic sail]

Pls help

idk what to do

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[kind crane]

both the solutions say that g must be divisible by 12

why is that? i dont understand

someone please explain this to me

[final saddle]

@kind crane Has your question been resolved?

[sturdy cypress]

divide by 2.4 is times 10 divide by 24

so you don't need it do be divisibe by 8 and 3, but only 4 and 3

because you get a 2 from multiplying by 10

maybe solution 2 is easier lemme see

well it's 12x divided by 5, and dividing by 5 doesn't mess with divisibility by 12

it's euclid's lemma if i'm not mistaken lol

given: 5 divides 12x
by euclid's lemma: if 5 divides 12x then 12 is divisible by 5, or x is divisible by 5
therefore x is divisible by 5

so x/5 is integer, so 12(x/5) is divisible by 12

and actually you already know x is divisible by 5

[final saddle]

@kind crane Has your question been resolved?

[final saddle]

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[oblique temple]

I need help on problem 34

I know my trig id's

I just don't know where to start 😅

I can see that I have to work on the left side, theirs nothing I can really do to the right side

[blissful meadow]

Use this on the numerator

[oblique temple]

is that a trig id

i mean, that looks interesting but i can't memorize that and use it for a test 💀

is their a simpler way?

What if I split the sin 3(theta) into sin (theta) and sin 2(theta)

[oblique temple]

does this make sense?

<@&286206848099549185>

[blissful meadow]

No you can't do that.

I would assume you would be given such identities if it came to that

[oblique temple]

I was only given sum and difference, double angle id's. The basic trig id's

not something super complicated lol so im puzzled how to do this problem

the sin 3(theta) is being a problem here on the numerator :/

[blissful meadow]

You can probably recover those identities using sum/difference

[oblique temple]

hmm ok

[blissful meadow]

Like maybe break it into sin(3x) = sin(2x+x)

Then use identity on that

[oblique temple]

ok ill try that

wait how do you use identity on sin(2x+x)

sin(2x+x) is not equal to sin(2x) + sin(x) right?

oh

i use a sum and difference id

[blissful meadow]

Yes

[oblique temple]

now i see how to do it

ill finish this problem up, ill ask you if i get stuck 😅

im stuck now :/

I got to this part

ill send a picture

a bit confused on what to do at this last step :/

should i have used a different double angle formula for cos(2x)

[blissful meadow]

It's fine. Now do the same thing with sin(x) = sin(2x - x)

[oblique temple]

which one

theirs 2 sin (x)

one at the front and one at the back

[blissful meadow]

The one with a minus

[oblique temple]

wait am i hallucinating

i still dont know which sin x

[blissful meadow]

Oh

mb

The one in the numerator

[oblique temple]

ill send picture

of what ive done so far

[oblique temple]

i did what you said over here

i did it

[blissful meadow]

Then you get terms that cancel

[oblique temple]

i finished the last part

[oblique temple]

yea

[blissful meadow]

And double angle in the denom

[oblique temple]

yupp

and i simplify that and get cos x = cos x

[oblique temple]

im gonna do 2 more trig id problems from here

@blissful meadow can you help me with problem 33

[oblique temple]

i dont know where to start here, left or right side 😅

[blissful meadow]

Left. Use Pythagorean identity, then difference of squares

[oblique temple]

okk

[oblique temple]

wait how do you use pythagoerean identity?

theirs no sec^2 (x) on the denominator

[blissful meadow]

Oh I was looking at 35

[oblique temple]

oh

Work on left side, multiply 1+sinx to numerator and denominotar?

[blissful meadow]

Yeah

[oblique temple]

okk

i got it

thanks, im done.

.closed

how do i close this 😅

.close

[final saddle]

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[delicate garden]

Can you see that this is the difference of two GP ?

[gentle zephyr]

I do not

[delicate garden]

Do you know about GP?

[gentle zephyr]

Geometric progression?

[delicate garden]

Yea tht

So

Rewrite

The first term as

(4^n )/( 9^n). * 1/9

[gentle zephyr]

Ok

[delicate garden]

now do you see GP?

Hint: rewrite it as (1/9) * (4/9)^n

[delicate garden]

Yea

[gentle zephyr]

I do not

[delicate garden]

Let's look at (4/9)^n first

So the terms will be?

[gentle zephyr]

Idk tbh

[delicate garden]

Do you see that the terms get multiplied by (4/9) ?

[delicate garden]

Yea

[gentle zephyr]

What is 'a' what is 'r'

[delicate garden]

a is the first term of the progression

And

[gentle zephyr]

4 /9 = a

[delicate garden]

r is not radius, it's the common ratio between two terms

[delicate garden]

Yea

[delicate garden]

OR the thing tht gets multiplied to the terms

[gentle zephyr]

r=1

[delicate garden]

No

(4/9)^2

Divide by

(4/9)

[gentle zephyr]

R = 4/9

A=?

[delicate garden]

Yea

[delicate garden]

a=4/9 also?

[gentle zephyr]

First term is (4/9)^(n-1) with n = 1 or..?

[delicate garden]

No

The nth term

Is

(4/9)^n

So

First term , n=1 is

4/9

[gentle zephyr]

And common ratio is 4/9 you multiply by that to progress

Mmm confusing but I think I get it now

[delicate garden]

Yea

So do you know the condition for convergence fo gp?

(I can tell you what the condition is but Idk how to formally prove the condition tho)

[delicate garden]

Yea

[gentle zephyr]

Absolute value of common ratio is <1

[delicate garden]

So use tht

[gentle zephyr]

,w |4/9|<1

[soft zealot]

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[gentle zephyr]

Both 3/4 < 1 and 4/9 < 1

[delicate garden]

Yea

So the whole thing converges

[delicate garden]

Now evaluate the sum, using this

[gentle zephyr]

(4/9)/(5/9)

36/45

[delicate garden]

4/5

[gentle zephyr]

, w 36/45 × 1/9 = 4/5

[soft zealot]

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[delicate garden]

Why 1/9

,w 36/45 = 4/5

[soft zealot]

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[gentle zephyr]

It's multiplied by 1/9 here

[delicate garden]

I seee

[gentle zephyr]

But I don't think it's part of the formula idk

[delicate garden]

Yea the 1/9 is a constant thats multiplied by the sum

So (4/5) * (1/9)

Is

4/45

Now do the other one

Then subtract

[gentle zephyr]

27/16

[delicate garden]

Heh?

[delicate garden]

,w (3/4) / ( 1-3/4)

[soft zealot]

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[delicate garden]

Times 3

So 9

[delicate garden]

1-3/4 is not 4/3

[gentle zephyr]

Is 1/4

I'm sorry

[delicate garden]

27/45 ???

[delicate garden]

Np bro everyone makes mistakes

[gentle zephyr]

3/5

[delicate garden]

,w (49)/(59*9)

[soft zealot]

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[delicate garden]

....

[gentle zephyr]

,w 4/45 - 9 = (1-135)/15

[soft zealot]

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[delicate garden]

,w 4/45 -9 = (4- 405)/45

[soft zealot]

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[gentle zephyr]

Thank you

I think I messed up my arithmetic though

Lol, but that's the least of the issues

[delicate garden]

Np

[gentle zephyr]

.solved

[final saddle]

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[final saddle]

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[shy grove]

guys, how to solve e^(1/2 ln9) without calculator?

[distant sleet]

well I mean firstly

how can you simplify 1/2ln9

[shy grove]

OOH

ln9^1/2

rightt

ln3

[shy grove]

thank youuuu

.close